The issue is that you're using a battle system to quantify her capabilities outside of that construct; the Bahamut battle in Advent Children is the most evident example of what the team does to handle a large-scale threat; if we applied this to Emerald Weapon, we should presume that all of the party members worked in unison to defeat it (now assuming they all wore the Underwater materia, or simply used the submarine to bombard it with torpedoes, which is actually much more likely). 

In the case of Tifa, we have her fight with Loz to ascertain what she can do; she is noticeably agile, an expert martial artist, and can propel herself into the air for great distances. Because she didn't use spirit energy in the fight (such as we see Cloud do repeatedly) we are either left to assume that she can't, and therefore her Limit Breaks are merely martial arts strikes, or she was defeated too quickly to do so. Given that her Final Heaven "punches with the force of a nuclear explosion" and she didn't use it Advent Children, the most reasonable translation is a spirit-charged superpunch over something that literally makes an atom bomb explosion.

That said, I use such spirit-based techs with her along with a few simple materia; all things equal, I am of the belief she is and always will be a mid-tier level fighter.